Solution:

Given:

- Initial temperature, \( T_1 = 27^\circ \text{C} = 300 \, \text{K} \)
- Final temperature, \( T_2 = 87^\circ \text{C} = 360 \, \text{K} \)
- Initial pressure, \( P_1 = 2 \, \text{atm} \)

Using the pressure-temperature relationship for a gas at constant volume:

\[
\frac{P_2}{P_1} = \frac{T_2}{T_1}
\]

Solving for \( P_2 \):

\[
P_2 = P_1 \times \frac{T_2}{T_1} = 2 \times \frac{360}{300} = 2 \times 1.2 = 2.4 \, \text{atm}
\]

Answer: \( P_2 = 2.4 \, \text{atm} \)